{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/optim/Gradient_Descent.ipynb)\n",
    "\n",
    "This example implements a basic gradient desscent optimizer to find minima in a potential function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.torch.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by defining a potential function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 288x216 with 2 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 288x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def potential(pos):\n",
    "    return math.cos(math.vec_length(pos))\n",
    "\n",
    "landscape = CenteredGrid(potential, x=100, y=100, bounds=Box(x=(-5, 5), y=(-5, 5)))\n",
    "plot(landscape, size=(4, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `math.gradient`, we can plot the gradient at each point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pot_grad = math.gradient(potential, 'pos', get_output=False)\n",
    "plot(landscape.with_values(pot_grad) * .2, size=(3, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's define a simple gradient descent step with step size $\\eta = 0.1$.\n",
    "To test it, we plot the optimization trajectory starting at $(1, 0)$ which should converge to towards $(\\pi,0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\phd\\phiflow2\\phiml\\phiml\\math\\_functional.py:600: RuntimeWarning: Using torch for gradient computation because numpy does not support jacobian()\n",
      "  warnings.warn(f\"Using {math.default_backend()} for gradient computation because {key.backend} does not support jacobian()\", RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 360x144 with 2 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gradient_descent_step(x):\n",
    "    return x - .1 * pot_grad(x)\n",
    "\n",
    "x0 = vec(x=1, y=0)\n",
    "opt_trj = iterate(gradient_descent_step, batch(iter=50), x0)\n",
    "plot(opt_trj.iter.as_spatial(), size=(5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's visualize the trajectories of all grid points. We have to change the dimension type to `batch` in order for the optimizations to work in parallel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x203062cef70>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = rename_dims(landscape.points, spatial, batch)\n",
    "opt_trj = iterate(gradient_descent_step, batch(iter=50), x0)\n",
    "plot([landscape, rename_dims(opt_trj, 'x,y', instance)], animate='iter', color='white', alpha=[1, .2], overlay='list', size=(6, 5))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
